Problem: $\dfrac{ -9k + l }{ 4 } = \dfrac{ -2k - 7m }{ 2 }$ Solve for $k$.
Answer: Multiply both sides by the left denominator. $\dfrac{ -9k + l }{ {4} } = \dfrac{ -2k - 7m }{ 2 }$ ${4} \cdot \dfrac{ -9k + l }{ {4} } = {4} \cdot \dfrac{ -2k - 7m }{ 2 }$ $-9k + l = {4} \cdot \dfrac { -2k - 7m }{ 2 }$ Reduce the right side. $-9k + l = {4} \cdot \dfrac{ -2k - 7m }{ {2} }$ $-9k + l = {2} \cdot \left( -2k - 7m \right)$ Distribute the right side $-9k + l = {2} \cdot \left( -{2k} - {7m} \right)$ $-9k + l = -{4}k - {14}m$ Combine $k$ terms on the left. $-{9k} + l = -{4k} - 14m$ $-{5k} + l = -14m$ Move the $l$ term to the right. $-5k + {l} = -14m$ $-5k = -14m - {l}$ Isolate $k$ by dividing both sides by its coefficient. $-{5}k = -14m - l$ $k = \dfrac{ -14m - l }{ -{5} }$ Swap signs so the denominator isn't negative. $k = \dfrac{ {14}m + {1}l }{ {5} }$